Old or Heavy? Decaying Gracefully with Age/Weight Shapes

Abstract

Modern saturation theorem provers are based on the givenclause algorithm, which iteratively selects new clauses to process. This clause selection has a large impact on the performance of proof search and has been the subject of much folklore. The standard approach is to alternate between selecting the oldest clause and the lightest clause with a fixed, but configurable age/weight ratio (AWR). An optimal fixed value of this ratio is shown to produce proofs significantly more quickly on a given problem, and further that varying AWR during proof search can improve upon a fixed ratio. Several new modes for the Vampire prover which vary AWR according to a "shape" during proof search are developed based on these observations. The modes solve a number of new problems in the TPTP benchmark set.

Layered Clause Selection for Theory Reasoning

“…This is a very significant result, suggesting the achieved control of theory reasoning is incredibly helpful. Moreover, one should keep in mind that strategies in a schedule are carefully selected to complement each other and even locally good changes in the strategies often destroy this complementarity (cf., e.g., [19,21]). In our case, however, we achieve an improvement despite this looming negative effect.…”

gym-saturation: an OpenAI Gym environment for saturation provers

“…There are many known feature engineering procedures. It can be as simple as clause age and weight [25], or information extracted from a clause syntax tree [18] or an inference lineage of a clause [30]. Representing logic formulae as such is an active research domain: for example, in [23], the authors proposed more than a dozen different embedding techniques based on formulae syntax.…”

Fully reusing clause deduction algorithm based on standard contradiction separation rule

“…Binary resolution proposed by Robinson has become the most well-known inference method due to its simplicity, reliability and efficiency, and research on the ATP systems based on binary resolution is still the mainstream research trend in this field. During the past few decades, many scholars have proposed a mass of different variants of binary resolution [19][20][21], e.g., linear resolution [22], locking resolution [23], sematic resolution [24], hyper resolution [25], and heuristic strategies based on binary resolution [26][27][28].…”